Finite Group Databasebeta

← C2×#11754213 #14479039

Subgroups — C2×#11754213 #14479039

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic30C211yesmaximal, characteristic
2C2×C5×#926C211yesmaximal, characteristic
3C2×C3×#4072C211yesmaximal, characteristic
4C2×#91532C214yesmaximal
5#11754213C2116yesmaximal, direct product factor
6C2×#91340C214yesmaximal, complemented
7C2×#91333C214yesmaximal, complemented
8C2×#65850—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×Dic15C2212yes—
11C22×Dic30C4116yescomplemented
12C22×Dic30C2212yes—
13C22×Dic30C2212yes—
14C22×Dic30C2218yes—
15C2×C5×#217C2212yes—
16C5×#926C2218yes—
17C2×C5×C4⋊Dic3C2212yes—
18C2×C4×C5×Dic3C2212yes—
19C2×C3×C22⋊Dic5C2212yes—
20C3×#4072C2218yes—
21C2×C3×C4⋊Dic5C2212yes—
22C2×C3×C4×Dic5C2212yes—
23C2×#6669C2218yes—
24#91532C22132yes—
25C2×Dic3×Dic5C2218yes—
26#91340C22132yescomplemented
27#91333C22132yescomplemented
28C2×#5516—51nomaximal, Hall
29C23×Dic10—31no—
30C2×C5×#117—31no—
31C2×#4072D311yescharacteristic
32#65850—316no—
33C2×#4033—34no—
34C2×#4023—34no—
35C2×C4×Dic10—34no—
36C24×C3×C5C2311yescharacteristic
37C22×C3×C4×C5C2×C418yes—
38C22×C3×C4×C5C2311yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×C3×C4×C5C2314yes—
41C22×Dic15C2×C4116yes—
42C22×Dic15C2314yes—
43C22×Dic15C2318yes—
44C2×Dic30C2×C4116yes—
45C2×Dic30C2×C4116yes—
46C2×Dic30C2×C4164yescomplemented
47C2×Dic30C2318yes—
48C2×Dic30C2318yes—
49C22×C5×Dic3C2314yes—
50C22×C3×Dic5C2314yes—
51C5×#217C2318yes—
52C5×C4⋊Dic3C2318yes—
53C4×C5×Dic3C2318yes—
54C3×C22⋊Dic5C2318yes—
55C3×C4⋊Dic5C2318yes—
56C3×C4×Dic5C2318yes—
57#6669C23132yes—
58Dic3×Dic5C23132yes—
59C23×Dic6—51no—
60C2×C3×#117—51no—
61C2×#926D511yescharacteristic
62#5516—516no—
63C2×#887—54no—
64C2×#877—54no—
65C2×C4×Dic6—54no—
66C23×C4×C5C2×D311yescharacteristic
67C23×Dic5—32no—
68C22×Dic10—316no—
69C22×Dic10—32no—
70C22×Dic10—32no—
71C22×Dic10—38no—
72C5×#117—38no—
73C2×C5×C4⋊C4—32no—
74C2×C5×C22⋊C4—32no—
75C2×C42×C5—32no—
76C2×C22⋊Dic5C2×D312yes—
77#4072C2×D318yes—
78C2×C4⋊Dic5C2×D312yes—
79C2×#683—38no—
80C2×C4×Dic5—38no—
81C2×C4×Dic5C2×D312yes—
82#4033—332no—
83#4023—332no—
84C4×Dic10—332no—
85C2×#519—151noSylow
86C23×C3×C5—24no—
87C23×C3×C5C22×C414yes—
88C23×C3×C5C2412yes—
89C23×C3×C5C2411yescharacteristic
90C2×C3×C4×C5C22×C414yes—
91C2×C3×C4×C5C22×C414yes—
92C2×C3×C4×C5C22×C4116yes—
93C2×C3×C4×C5C2412yes—
94C2×C3×C4×C5C2412yes—
95C2×Dic15C22×C4116yes—
96C2×Dic15C22×C4132yes—
97C2×Dic15C2418yes—
98Dic30C22×C4132yes—
99Dic30C22×C4132yes—
100C2×C5×Dic3—28no—
101C2×C5×Dic3C2418yes—
102C2×C3×Dic5—28no—
103C2×C3×Dic5C2418yes—
104C23×C3×C4C2×D511yescharacteristic
105C23×Dic3—52no—
106C22×Dic6—516no—
107C22×Dic6—52no—
108C22×Dic6—52no—
109C22×Dic6—58no—
110C3×#117—58no—
111C2×C3×C4⋊C4—52no—
112C2×C3×C22⋊C4—52no—
113C2×C3×C42—52no—
114C2×#217C2×D512yes—
115#926C2×D518yes—
116C2×C4⋊Dic3C2×D512yes—
117C2×Dic3⋊C4—58no—
118C2×C4×Dic3—58no—
119C2×C4×Dic3C2×D512yes—
120#887—532no—
121#877—532no—
122C4×Dic6—532no—
123C24×C5C22×D311yescharacteristic
124C22×C4×C5—34no—
125C22×C4×C5C4×D318yes—
126C22×C4×C5C22×D311yescharacteristic
127C22×C4×C5C22×D311yescharacteristic
128C22×C4×C5C22×D314yes—
129C22×Dic5—316no—
130C22×Dic5—38no—
131C22×Dic5—34no—
132C22×Dic5C22×D314yes—
133C2×Dic10—316no—
134C2×Dic10—316no—
135C2×Dic10—364no—
136C2×Dic10—38no—
137C2×Dic10—38no—
138C5×C4⋊C4—38no—
139C5×C22⋊C4—38no—
140C42×C5—38no—
141C22⋊Dic5C22×D318yes—
142C4⋊Dic5C22×D318yes—
143#683—332no—
144C4×Dic5—332no—
145C4×Dic5C22×D318yes—
146C23×Q8—151no—
147#519—1516no—
148C2×C4×Q8—154no—
149C2×C4×Q8—154no—
150C2×#117—31no—
151C2×#117—51no—
152C2×#117—154no—
153C22×C3×C5—28no—
154C22×C3×C5—24no—
155C22×C3×C5C23×C414yes—
156C22×C3×C5C23×C412yes—
157C22×C3×C52−1+414yes—
158C22×C3×C5C2511yescharacteristic
159C3×C4×C5C23×C414yes—
160C3×C4×C5C23×C414yes—
161Dic15C23×C4116yes—
162C3×Dic5—28no—
163C5×Dic3—28no—
164C24×C3C22×D511yescharacteristic
165C22×C3×C4—54no—
166C22×C3×C4C4×D518yes—
167C22×C3×C4C22×D511yescharacteristic
168C22×C3×C4C22×D511yescharacteristic
169C22×C3×C4C22×D514yes—
170C22×Dic3—516no—
171C22×Dic3—58no—
172C22×Dic3—54no—
173C22×Dic3C22×D514yes—
174C2×Dic6—516no—
175C2×Dic6—516no—
176C2×Dic6—564no—
177C2×Dic6—58no—
178C2×Dic6—58no—
179C3×C4⋊C4—58no—
180C3×C22⋊C4—58no—
181C3×C42—58no—
182#217C22×D518yes—
183C4⋊Dic3C22×D518yes—
184Dic3⋊C4—532no—
185C4×Dic3—532no—
186C4×Dic3C22×D518yes—
187C23×C5—24no—
188C23×C5C2×C4×D314yes—
189C23×C5C23×D312yes—
190C23×C5C23×D311yescharacteristic
191C2×C4×C5—38no—
192C2×C4×C5—68no—
193C2×C4×C5C2×C4×D3116yes—
194C2×C4×C5C2×C4×D314yes—
195C2×C4×C5C2×C4×D314yes—
196C2×C4×C5C23×D312yes—
197C2×C4×C5C23×D312yes—
198C2×Dic5—28no—
199C2×Dic5—332no—
200C2×Dic5—316no—
201C2×Dic5—38no—
202C2×Dic5C23×D318yes—
203Dic10—332no—
204Dic10—332no—
205C22×Q8—1516no—
206C22×Q8—152no—
207C22×Q8—152no—
208C22×Q8—158no—
209C23×C4—152no—
210C23×C4D3×D511yescharacteristic
211C4×Q8—1532no—
212C4×Q8—1532no—
213#117—38no—
214#117—58no—
215#117—1532no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—52no—
218C2×C4⋊C4—158no—
219C2×C22⋊C4—32no—
220C2×C22⋊C4—52no—
221C2×C42—32no—
222C2×C42—52no—
223C2×C42—158no—
224C2×C3×C5—24no—
225C2×C3×C5#51914yescomplemented
226C2×C3×C5C24×C411yescharacteristic
227C2×C3×C5C2×2−1+412yes—
228C23×C3—24no—
229C23×C3C2×C4×D514yes—
230C23×C3C23×D512yes—
231C23×C3C23×D511yescharacteristic
232C2×C3×C4—58no—
233C2×C3×C4—108no—
234C2×C3×C4C2×C4×D5116yes—
235C2×C3×C4C2×C4×D514yes—
236C2×C3×C4C2×C4×D514yes—
237C2×C3×C4C23×D512yes—
238C2×C3×C4C23×D512yes—
239C2×Dic3—28no—
240C2×Dic3—532no—
241C2×Dic3—516no—
242C2×Dic3—58no—
243C2×Dic3C23×D518yes—
244Dic6—532no—
245Dic6—532no—
246C22×C5—24no—
247C22×C5—28no—
248C22×C5C22×C4×D314yes—
249C22×C5C22×C4×D312yes—
250C22×C5#101014yes—
251C22×C5C24×D311yescharacteristic
252C4×C5—68no—
253C4×C5C22×C4×D314yes—
254C4×C5C22×C4×D314yes—
255Dic5—28no—
256Dic5—316no—
257C24C2×D3×D511yescharacteristic
258C2×Q8—1516no—
259C2×Q8—1516no—
260C2×Q8—1564no—
261C2×Q8—158no—
262C2×Q8—158no—
263C22×C4—34no—
264C22×C4—54no—
265C22×C4—1516no—
266C22×C4—158no—
267C22×C4—154no—
268C22×C4#120018yes—
269C22×C4C2×D3×D514yes—
270C22×C4C2×D3×D511yescharacteristic
271C22×C4C2×D3×D511yescharacteristic
272C4⋊C4—38no—
273C4⋊C4—58no—
274C4⋊C4—1532no—
275C22⋊C4—38no—
276C22⋊C4—58no—
277C42—38no—
278C42—58no—
279C42—1532no—
280C3×C5C2×#51911yescharacteristic, complemented, Hall
281C22×C3—28no—
282C22×C3—24no—
283C22×C3C22×C4×D514yes—
284C22×C3C22×C4×D512yes—
285C22×C3#415014yes—
286C22×C3C24×D511yescharacteristic
287C3×C4—108no—
288C3×C4C22×C4×D514yes—
289C3×C4C22×C4×D514yes—
290Dic3—28no—
291Dic3—516no—
292C2×C5—24no—
293C2×C5#551614yescomplemented
294C2×C5C23×C4×D311yescharacteristic
295C2×C5C2×#101012yes—
296C23—24no—
297C23C2×#120014yes—
298C23C22×D3×D512yes—
299C23C22×D3×D511yescharacteristic
300Q8—1532no—
301Q8—1532no—
302C2×C4—38no—
303C2×C4—58no—
304C2×C4—68no—
305C2×C4—108no—
306C2×C4—1532no—
307C2×C4—1516no—
308C2×C4—158no—
309C2×C4C2×#1200116yes—
310C2×C4C2×#120014yes—
311C2×C4C2×#120014yes—
312C2×C4C22×D3×D512yes—
313C2×C4C22×D3×D512yes—
314C2×C3—24no—
315C2×C3#6585014yescomplemented
316C2×C3C23×C4×D511yescharacteristic
317C2×C3C2×#415012yes—
318C5C2×#551611yescharacteristic, complemented, Sylow
319C22—24no—
320C22—28no—
321C22#9200114yes—
322C22C22×#120014yes—
323C22C22×#120012yes—
324C22C23×D3×D511yescharacteristic
325C4—68no—
326C4—108no—
327C4—1516no—
328C4C22×#120014yes—
329C4C22×#120014yes—
330C3C2×#6585011yescharacteristic, complemented, Sylow
331C2—24no—
332C2#1175421314yesdirect product factor
333C2C2×#9200112yes—
334C2C23×#120011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC22×C3×C5C25
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #11754213C2direct (N × H)
6. C2×#91340C2semidirect
7. C2×#91333C2semidirect
11. C22×Dic30C4semidirect
26. #91340C22semidirect
27. #91333C22semidirect
46. C2×Dic30C2×C4semidirect
225. C2×C3×C5#519semidirect
280. C3×C5C2×#519semidirect
293. C2×C5#5516semidirect
315. C2×C3#65850semidirect
318. C5C2×#5516semidirect
330. C3C2×#65850semidirect
332. C2#11754213direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×Dic302
C2×C5×#9262
C2×C3×#40722
C2×#915322
#117542132
C2×#913402
C2×#913332
C2×#658503
C2×#55165